The lengths of lumber a machine cuts are normally distributed with a mean of 90 inches and a standard deviation of 0.3 inch.(a) What is the probability that a randomly selected board cut by the machine has a length greater than 90.07 inches?(b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 90.07 inches?.....(a) The probability is 0.4078 .(Round to four decimal places as needed.)(b) The probability is(Round to four decimal places as needed.)

GivenMean(μ)=90standard deviation(σ)=0.3

Answered: The lengths of lumber a machine cuts…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 8 ounces. a. The process standard deviation is 0.10, and the process control is set at plus or minus 2 standard deviations. Units with weights less than 7.8 or greater than 8.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to 0.08. Assume the process control remains the same, with weights less than 7.8 or greater than 8.2 ounces being classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)? c. What is the advantage of reducing process…
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the person is between 62 and 63.9 inches. c. The middle 40% of Martian heights lie between what two numbers? Low: inches High: inches
The average amount of money spent for lunch per person in the college cafeteria is $5.99 and the standard deviation is $2.1. Suppose that 49 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. For the group of 49 patrons, find the probability that the average lunch cost is between $5.77 and $6.08.
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1) The mean and standard deviation of a population are 200 and 20, respectively.The probability of selecting one data value less than 190 is ____ %. (Round answer to the nearest percent (whole number). Do not write the % sign.) 2) A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours.If 20 children between the ages of 2 and 5 are randomly selected, the number of children in the sample who watch at least 25.2 hours of television is? Give answer to the nearest whole number, not a percent. 3) A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours.If 20 children between the ages of 2 and 5 are randomly selected, the number of children in the sample who watch at most 22.5 hours of television is? . Give…

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